• Journal of Institute of Control, Robotics and Systems
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• v.6 no.5
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• pp.356-366
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• 2000

In this paper, a nonlinear $H_2/H_\infty/LTR$ control for the flexible inverted pendulum of a parallel type with Coulomb friction is presented. The dynamic equation for this system is derived by the Hamilton's principle and assumed-mode method. This hard nonlinear system can be modeled by a the quasi-linear state space model using the REF method. It is shown that the $H_2/H_\infty$ control can be applied to the nonlinear controller design of the system having Coulomb frictions if the proper LTR conditions are satisfied. In order to present the usefulness of the suggested control method, the nonlinear $H_2/H_\infty/LTR$ controller is designed to control the Position of the end point of the flexible inverted pendulum that has Coulomb frictions present in actuator parts. The results are given via computer simulations.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.331-331
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• 2000

This paper presents the mixed $H_2/H_{\infty}$ output feedback controIler design method for linear systems with delayed state. The objective is to design the output feedback controller which minimizes the H$_2$-norm of one transfer function while ensuring the H$_{\infty}$-norm of the other is held below a chosen level. When objective is tormulated in terms of a common Lyapunov function, the sufficient conditions of existence of mixed $H_2/H_{\infty}$ controller are given in terms of LMIs. terms of LMIs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.2
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• pp.276-281
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• 2008

This paper proposes a new sliding surface which can have the same dynamics of nominal system based on SVM(Support Vector Machines). The conventional sliding mode control can not have the properties of $H_{\infty}$ controller because its sliding surface has lower order dynamics than the original system. The additional states must be used to solve this problem. However, The sliding surface of this paper can have the dynamics of $H_{\infty}$ control system by using support vector machines without defining any additional dynamic state. By using SVM, the property of $H_{\infty}$ control system can be estimated as a relationship between the states. With this relationship, a new sliding surface can be designed and have $H_{\infty}$ control system properties. As a result, in spite of the parameter uncertainty, the proposed controller can have the same dynamic of nominal system controlled by $H_{\infty}$ controller.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.37 no.5
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• pp.103-110
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• 2000

In This paper, we propose a design procedure for a SD $H_{\infty}$controller with PID performance. In developing the procedure, we use the basic idea of standard$H_{\infty}$problem, and then applied it to the SD system, which consists of the continuous plant and the discrete controller. This $H_{\infty}$controller design procedure involves the selections of weighting functions. The selections considered the relation of the closed loop specification between the $H_{\infty}$controller and PID. We illustrate this procedure in the controller design for a two-mass spring system.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.7
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• pp.578-583
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• 2002

This paper presents a method for designing fuzzy $H_2/H_{\infty}$ controllers of nonlinear systems with time varying delay. Takagi-Sugeno fuzzy model is employed to represent nonlinear systems with time varying delay. Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMls). The proposed fuzzy $H_2/H_{\infty}$ controllers minimizes the upper bound on the linear quadratic performance measure.

• International Journal of Control, Automation, and Systems
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• v.1 no.2
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• pp.206-209
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• 2003

An $H_2$/$H_{\infty}$ -controller realization is carried out by considering an entropy integral. Using J-spectral factorization, the parametrizations of all $H_{\infty}$ stabilizing controllers are derived. By the relation of a mixed $H_2$/$H_{\infty}$ control problem and a minimum entropy/$H_{\infty}$ control problem, the mixed $H_2$/$H_{\infty}$-controller state-space realization is presented.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.868-873
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• 2003

$H_{\infty}$ control has been applied to the design of practical control systems widely because of its robustness. It can minimize $H_{\infty}$ norm of the transfer function between the desired output and the disturbances. The SMC(Sliding Mode Control) is more robust and give the better performance than the $H_{\infty}$ control if the matching condition is satisfied. A controller which can have the advantages of $H_{\infty}$ control and the SMC is proposed to add the robustness of the SMC to the $H_{\infty}$ controller. Its design is based on the augmented system of which dynamics have one higher order than that of the original system and has the same dynamic as the desired system in spite of uncertainties. The dynamic of proposed sliding surface is the same dynamic as the system controlled by $H_{\infty}$ controller without the uncertainties which satisfy the matching condition.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.88-91
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• 1999

The purpose of this paper is to propose an approach to design a robust servo controller based on the Mixed H$_2$/H$\sub$$\infty$/ theory. In order to do this, we first modify the generalized plant for the usual H$\sub$$\infty$/ servo problem to a structure of the Mixed H$_2$/H$\sub$$\infty$/ minimization problem by virtue of the internal model principle. By doing this, we can divide specifications adopted for robust servo system design into H$_2$and H$\sub$$\infty$/ performance criteria, respectively. Then, the mixed H$_2$/H$\sub$$\infty$/ problem is solved in order to find the best solution, by which we can minimize H$_2$-norm of the transfer function under the condition of H$\sub$$\infty$/-norm value, through Linear Matrix Equality (LMI).

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.529-534
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• 2005

In this paper, a new type of output feedback control, called a $H_2/H_{\infty}$ fnite memory control (FMC), is proposed for deterministic state space systems. Constraints such as linearity, unbiasedness property, and finite memory structure with respect to an input and an output are required in advance to design $H_2/H_{\infty}$ FMC in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FMC design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMIs) with some linear equality constraints. Through simulation study, it is illustrated that the proposed $H_2/H_{\infty}$ FMC is more robust against uncertainties and faster in convergence than the existing $H_2/H_{\infty}$ output feedback control schemes.

• Journal of Power System Engineering
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• v.2 no.2
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• pp.41-46
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• 1998

This paper presents the vibration control for the two degree-of-freedom which is a reduced model of multi-layer structure. This reduced model is designed for the first and second order resonance in the low frequency domain where the disturbance such as the earth quake has the large energy. And a designed controller using the LQ type $H_{\infty}$ control theory shows the good performance for the impulse disturbance through the experimental results and the simulation results respectively.